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User blog:Edwin Shade/The Comprehensive List Of Googologists
This list encompasses any and all googologists who have made a contribution to the field of Googology either in a large way, or in a small way. To be included on the list, their contributions have to be significant enough to merit attention by a portion of the community, and not just by one or two individuals. The list is presented in a roughly chronological order. Before the Wikia Archimedes of Syracuse (c.287 - c.212 B.C.) Archimedes was one of the first individuals to venture beyond the everyday numbers people frequently dealt with and go about creating large numbers for the sake of it. In his famous paper The Sand Reckoner, Archimedes invented a system of naming numbers that is capable of expressing the number of grains of sand that can fit into the universe, (taking into account of course that Archimedes assumed the universe to only be 10^{14} stadia, or about 2 light years). The largest number he named in his system was 10^{8\cdot{10^{16}}} , which is inbetween a googol and a googolplex. Hugo Steinhaus (1887 - 1972) Steinhaus, pictured above, was a professor at the Jan Kazimierz University in Lwów, and got his PhD under the famous David Hilbert. Steinhaus created a polygonal notation which had a upper growth rate comparable to f_4(n) in the fast-growing hierarchy. Leo Moser (1921 - 1970) Moser was an Austrian-Canadian mathematician who spent most of his teaching years at the University of Alberta. He extended Steinhaus' polygonal notation to form the complete Steinhaus-Moser notation, which was able to produce numbers comparable to f_{\omega}(n) in the fast-growing hierarchy. Moser's number is named after him. Donald Knuth (1938 - present) Donald Knuth is a retired professor at Standford University, and has made many contributions to the field of Computer Programming. In Googology he is most famous for his up-arrow notation, which has a strength roughly equal to that of Steinhaus-Moser notation. Knuth's up-arrow notation was invented in 1976 in an attempt to be able to describe very large numbers with a simple description. Ronald Graham (1935 - present) Ronald graham worked at AT&T Labs for 37 years, and was president of the American Mathematical Society between 1993 and 1994, as well as past president of the International Jugglers' Association. Graham's number, perhaps the most widely recognized googologism besides the googol and googolplex, is a number that was created by Ronald Graham as an upper bound of a problem concerning hyper-dimensional cubes. Since the time he came up with his number the upper bound has been reduced to 2\uparrow\uparrow\uparrow 6 , vastly smaller than the original number, which though an outdated upper bound, has been used no less by people in it's popularity. Wilhelm Ackermann (1896 - 1962) Wilhelm Ackermann was a German mathematician who collaborated with David Hilbert. He is well-known for his Ackermann Function, which is one of the earliest examples of a total computable function that is not primitive recursive. Ackermann's function is important in Googology due to it's large output of numbers for small inputs; the function has two inputs. The Ackermann ordinal is named after him, and is equal to \varphi(1,0,0,0) in Veblen notation. [List is to be continued. If you feel like you belong on this list, please provide a reason why, and I will most likely put you on the list eventually. If you have any recommendations as to how this list might be improved, also feel free to leave them in the comment section below.] . Category:Blog posts